Computing the implied volatility in stochastic volatility models

  title={Computing the implied volatility in stochastic volatility models},
  author={Henri Berestycki and J{\'e}r{\^o}me Busca and Igor Florent},
  journal={Communications on Pure and Applied Mathematics},
The Black-Scholes model [6, 23] has gained wide recognition on financial markets. One of its shortcomings, however, is that it is inconsistent with most observed option prices. Although the model can still be used very efficiently, it has been proposed to relax its assumptions, and, for instance, to consider that the volatility of the underlying asset S is no longer a constant but rather a stochastic process. There are two well-known approaches to achieve this goal. In the first class of models… 

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